Thermodynamics HW Solutions 364 - Chapter 4 Transient Heat...

Chapter 4 Transient Heat Conduction 4-84 A cylindrical aluminum block is heated in a furnace. The length of time the block should be kept in the furnace and the amount of heat transferred to the block are to be determined. Assumptions 1 Heat conduction in the cylindrical block is two-dimensional, and thus the temperature varies in both axial x- and radial r-directions. 2 Heat transfer from the bottom surface of the block is negligible. 3 The thermal properties of the aluminum are constant. 4 The heat transfer coefficient is constant and uniform over the entire surface. 5 The Fourier number is τ > 0.2 so that the one-term approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified). Properties The thermal properties of the aluminum block are given to be k = 236 W/m. ° C, ρ = 2702 kg/m 3 , C p = 0.896 kJ/kg. ° C, and α = 9.75 × 10-5 m 2 /s. Analysis

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